Update on Overleaf.

1 files changed, 171 insertions, 65 deletions

diff --git a/response.txt b/response.txt
index e9337dd..058a6f8 100644
--- a/response.txt
+++ b/response.txt
@@ -1,40 +1,119 @@
+\documentclass[a4paper]{letter}
 
-Because neither referee addressed the scientific content of our paper,
-nor substantively addressed its presentation, we have not submitted a
-revised manuscript. Below, we respond to the referees' comments.
-
-Report of Referee A -- LY17256/Kent-Dobias
-> The authors consider spin glass models with mixed p-spin interactions
-> on the N-Sphere and calculate the number of stationary points, the
-> logarithm of which yields the complexity. The disorder average of this
-> logarithm is computed with the replica trick, and for different model
-> variants different replica symmetry breaking (RSB) solutions are
-> obtained. A new feature of the solutions, in contrast to previous
-> replica symmetric calculations, is that RSB must occur in parts of the
-> energy-stability phase diagram.
->
-> The paper is clearly written although the content is rather technical
-> and probably only accessible to experts in mean field spin glass
-> models and the different RSB schemes developed in this field. In
-> connection with the well-studied p=3 spin glass model it is briefly
-> mentioned that the complexity and its transitions as a function of
-> energy and/or stability is relevant for the equilibrium and the
-> dynamical behavior of this model – but such a connection has not been
-> made here.
->
-> Therefore, I feel that the results presented here are only interesting
-> for group of experts and I do not assess the finding that the
-> complexity of mixed p-spin glass models shows RSB as a major
-> breakthrough in the field. Therefore, the manuscript is not suitable
-> for publication in Phys. Rev. Lett., and the publication of the
-> accompanying longer paper, submitted to PRE, is sufficient to
-> disseminate the results summarized in this manuscript.
-
-Referee A says that our paper is clearly written but technical, and
+\usepackage[utf8]{inputenc} % why not type "Bézout" with unicode?
+\usepackage[T1]{fontenc} % vector fonts plz
+\usepackage{newtxtext,newtxmath} % Times for PR
+\usepackage[
+  colorlinks=true,
+  urlcolor=purple,
+  linkcolor=black,
+  citecolor=black,
+  filecolor=black,
+]{hyperref} % ref and cite links with pretty colors
+\usepackage{xcolor}
+\usepackage[style=phys]{biblatex}
+
+\renewcommand{\thefootnote}{\fnsymbol{footnote}}
+
+\addbibresource{frsb_kac-rice.bib}
+
+\signature{
+  \vspace{-6\medskipamount}
+  \smallskip
+  Jaron Kent-Dobias \& Jorge Kurchan
+}
+
+\address{
+  Laboratoire de Physique\\
+  Ecole Normale Sup\'erieure\\
+  24 rue Lhomond\\ 
+  75005 Paris
+}
+
+\begin{document}
+\begin{letter}{
+  Agnese I.~Curatolo, Ph.D.\\
+  Physical Review Letters\\
+  1 Research Road\\
+  Ridge, NY 11961
+}
+
+\opening{Dear Dr.~Curatolo,}
+
+
+Because neither referee addressed (or criticized)  the scientific content of our paper,
+nor substantively addressed its presentation, we have only modified
+the manuscripts in order to highlight the importance of having a full solution. 
+
+
+We have thus added the paragraph:
+
+{\color{red} 
+Having  a full, exact  (`quenched') solution of the generic problem  is not 
+primarily a matter of {\em accuracy}.
+Very basic structural questions are omitted in the approximate `annealed' solution. What is lost  is  the nature, at any given
+energy (or free energy) level, of the stationary points in a generic energy function: at low energies are they basically all minima, with  an exponentially small number of saddles, or
+-- as we show here -- do they consist of a mixture of saddles whose index -- the number of unstable directions -- is a smoothly distributed number? 
+These questions need to be answered for the understanding of the relevance of more complex objects such as
+barrier crossing (which barriers?) \cite{Ros_2019_Complexity, Ros_2021_Dynamical}, or the fate of long-time dynamics
+(which end in what kind of  target states?). 
+
+}
+
+Both referees find that our paper is clearly written but technical, and
 that its topic of "the different RSB schemes" are not suitable for a
 broad audience. This is surprising to the authors, since a quick
 search on Google Scholar reveals several recent PRLs with heavy use of
-RSB schemes.
+RSB schemes. 
+
+We would also like to submit to the referees  that it is somewhat
+incongruous that the solution to a problem that had remained open for 42 years -- during which it was always present in articles in PRL and PRX -- is rejected
+because  it demands of the readers a slightly longer attention span. 
+
+
+
+
+\begin{enumerate}
+  \item PRL has been publishing articles on precisely this problem in the
+    last 30 years.\footfullcite{Fyodorov_2004_Complexity, Bray_2007_Statistics, Fyodorov_2012_Critical, Wainrib_2013_Topological}
+  \item These works were often limited by the fact that general landscapes (for
+    which an annealed solution is not exact) were inaccessible. It is perhaps
+    true that the final solution of an open problem may often be more technical
+    than the previous ones.
+\end{enumerate}
+
+
+
+Below, we respond to the referees' comments.
+
+{\it Report of Referee A -- LY17256/Kent-Dobias
+ The authors consider spin glass models with mixed p-spin interactions
+ on the N-Sphere and calculate the number of stationary points, the
+ logarithm of which yields the complexity. The disorder average of this
+ logarithm is computed with the replica trick, and for different model
+ variants different replica symmetry breaking (RSB) solutions are
+ obtained. A new feature of the solutions, in contrast to previous
+ replica symmetric calculations, is that RSB must occur in parts of the
+ energy-stability phase diagram.
+
+ The paper is clearly written although the content is rather technical
+ and probably only accessible to experts in mean field spin glass
+ models and the different RSB schemes developed in this field. In
+ connection with the well-studied p=3 spin glass model it is briefly
+ mentioned that the complexity and its transitions as a function of
+ energy and/or stability is relevant for the equilibrium and the
+ dynamical behavior of this model – but such a connection has not been
+ made here.
+
+ Therefore, I feel that the results presented here are only interesting
+ for group of experts and I do not assess the finding that the
+ complexity of mixed p-spin glass models shows RSB as a major
+ breakthrough in the field. Therefore, the manuscript is not suitable
+ for publication in Phys. Rev. Lett., and the publication of the
+ accompanying longer paper, submitted to PRE, is sufficient to
+ disseminate the results summarized in this manuscript.}
+
+
 
 Referee A correctly points out that one new feature of the solutions
 outlined in our manuscript is that RSB must occur in parts of the
@@ -42,10 +121,12 @@ phase diagram for these models. However, they neglect another feature:
 that they are the solutions of the *quenched* complexity, which has
 not been correctly calculated until now. We agree with the referee
 that "the complexity of the mixed p-spin glass models" is not a major
-breakthrough in and of itself, but believe that the technique for
-computing the quenched complexity is a major breakthrough. Just
-because this new technique is demonstrated on the simplest toy models
-should not discount its importance and potential.
+breakthrough in and of itself, we just
+chose to demonstrate  the problem in simplest toy model. But believe that the technique for
+computing the quenched complexity is a major breakthrough  
+{\bf because it brings in the features of organization of saddles of all
+kinds that are invisible in the annealed scheme}. 
+
 
 Referee A states that a connection between the complexity and the
 equilibrium and dynamical behavior is not made in our paper. Until
@@ -55,38 +136,55 @@ spherical models was exciting enough news to be published in PRX 10,
 031045 (2020). It is true that our work doesn't solve the problem that
 paper opened, but it does deepen it by showing definitively that the
 use of RSB and the quenched complexity are not sufficient to
-reestablish a landscape–dynamics connection. We disagree with the
-referee's implicit assertion that only clean resolutions, and not the
-compelling deepening of problems, are worthy of a broad audience.
+reestablish a landscape–dynamics connection. 
+{\bf One can hardly expect that the structure of saddles at a given energy may be connected
+with dynamics (for example in Sherrington Kirkpatrick) if it is unknown}.
+%We disagree with the
+%referee's implicit assertion that only clean resolutions, and not the
+%compelling deepening of problems, are worthy of a broad audience.
 
 Report of Referee B -- LY17256/Kent-Dobias
-> The paper presents a computation of the complexity in spherical
-> spin-glass models. Neither the techniques nor the results are
-> sufficiently new and relevant to justify publication on PRL. This is
-> not surprising given that the topic has been studied extensively in
-> the last thirty years and more, the only novelty with respect to
-> previous work is that the results are obtained at zero temperature but
-> this is definitively not enough. Essential open problems in the field
-> involves dynamics and activated processes and some results have
-> appeared recently, instead the analysis of the static landscape, to
-> which the present paper is a variation, failed to deliver answers to
-> these questions up to now.
->
-> I recommend that the paper is not published in PRL while the companion
-> paper is worth publishing on PRE.
-
-We disagree with the statement of Referee B that "the only novelty
+{\it  The paper presents a computation of the complexity in spherical
+ spin-glass models. Neither the techniques nor the results are
+ sufficiently new and relevant to justify publication on PRL. This is
+ not surprising given that the topic has been studied extensively in
+ the last thirty years and more, the only novelty with respect to
+ previous work is that the results are obtained at zero temperature but
+ this is definitively not enough. Essential open problems in the field
+ involves dynamics and activated processes and some results have
+ appeared recently, instead the analysis of the static landscape, to
+ which the present paper is a variation, failed to deliver answers to
+ these questions up to now.
+
+ }
+
+Concerning the statement of Referee B that "the only novelty
 with respect to previous work is that the results are obtained at zero
-temperature". For a system where the quenched and annealed
-complexities differ, there has not been a correct calculation of the
-quenched complexity at finite temperature. (and, besides our work,
-only once or twice at zero temperature, e.g., PRX 9, 011003 (2019).)
-Rejecting a paper based on a severe misconception of its contents or
-of the state of the field is not appropriate.
-
-We agree with Referee B's assessment of "[e]ssential open problems in
+temperature", we do not know what to make of the referee's statement.
+The novelty of the paper is most definitely
+not the fact of treating a zero temperature case. 
+We have added the following phrase, that should clarify the situation:
+
+{\color{blue}
+  For simplicity we have concentrated here on the energy, rather
+than  {\em free-energy} landscape, although the latter is sometimes
+more appropriate. From the technical point of view, this makes no fundamental difference, it suffices 
+to apply the same computation to the Thouless-Andreson-Palmer \cite{Crisanti_1995_Thouless-Anderson-Palmer} (TAP) free energy, instead of the energy. We do not expect new features or technical 
+complications arise.
+
+}
+
+
+%For a system where the quenched and annealed
+%complexities differ, there has not been a correct calculation of the
+%quenched complexity at finite temperature. (and, besides our work,
+%only once or twice at zero temperature, e.g., PRX 9, 011003 (2019).)
+%Rejecting a paper based on a severe misconception of its contents or
+%of the state of the field is not appropriate.
+
+We agree with Referee B's assessment of "essential open problems in
 the field," and agree that our work does not deliver answers. However,
-delivering answers for essential open problems is not the acceptance
+delivering answers for all essential open problems is not the acceptance
 criterion of PRL. These are
 
   - Open a new research area, or a new avenue within an established area.
@@ -100,3 +198,11 @@ dynamics. We believe that its essential step is through the
 introduction of a new technique, calculation of the quenched
 complexity, which we believe will have significant impact as it is
 applied to more complicated models.
+
+\closing{Sincerely,}
+
+\vspace{1em}
+
+\end{letter}
+
+\end{document}